This invention relates to pressure transducer designs and methods for selecting the dimensions and geometry of force-producing pressure elements such that spurious modes of oscillation do not coincide with the frequencies generated by force-sensitive resonators that are used to measure the applied pressures.
A number of force-sensitive resonators are described in the prior art. Single vibrating beam force sensors are described in U.S. Pat. Nos. 3,470,400, 3,479,536, 4,445,065, 4,656,383, 4,658,174, 4,658,175, 4,743,790, 4,980,598, 5,109,175, and 5,596,145. Double vibrating beam force sensors, referred to as Double-Ended Tuning Forks (DETF), are described in U.S. Pat. Nos. 3,238,789, 4,215,570, 4,415,827, 4,469,979, 4,531,073, 4,757,228, and 4,912,990. Each of these patents describes a resonator to which a force, which may be induced by pressure, is applied. The force alters the resonant frequency of the resonator so that the frequency of oscillation is indicative of the magnitude of the applied force. FIG. 1 is an isometric view of a force-sensitive transducer made with a conventional Double-Ended Tuning Fork (DETF), as described in U.S. Pat. No. 4,372,173. The DETF includes a pair of parallel beams 3 extending between a pair of mounting pads 1, 2. The mounting pads 1, 2 are attached to respective mounting structures 9, 7 by suitable means. Axial forces, applied along a longitudinal axis of the transducer extending between the mounting pads 1, 2 stress the beams 3, thereby changing the resonant frequency at which they vibrate in accordance with the magnitude of the applied force. The beams 3 are preferably fabricated using a piezoelectric material, such as quartz, and they are driven through piezoelectric excitation by an electrode pattern 15 placed on the beams 3. The electrode pattern 15 is coupled to contacts 11, 13 formed on the mounting pad 2, which are, in turn, coupled to oscillator circuitry (not shown). The oscillator circuitry is designed to drive the beams 3 at their resonant frequency. Alternative means of excitation include passing an electrical current at the resonant frequency through the beams in a magnetic field or capacitive drive means. The transducer achieves low energy loss because most reactive moments and forces which might be transmitted to the mounting structures 7, 9 are cancelled by the beams 3 being driven 180 degrees out of phase.
The resonant frequency fo of the unstressed double-ended tuning fork beam of length L, tine thickness in the direction of vibration t, tine width b, modulus of elasticity E, and density d, is given by the formula:
fo=(constant)(t /L2)(E/d)
FIG. 2 is a graph that shows the change of the resonant frequency as a function of applied load. If the load is in compression, the resonant frequency decreases. Under tensile load, the resonant frequency increases. The resonator in the shown example changes frequency by approximately 10% under full-scale load.
Although the resonant frequency is generally a non-linear function of the applied load F, the change in frequency under load may be approximated by:
f=fo(1+a*F)
Where
a=(constant)L2/(E*t3*b)
The load on the resonator may be either compressive or tensile, causing a frequency decrease or increase, respectively. Thus the sign of the constant a can be positive or negative. The resonant frequency, f, will vary between a minimum, fmin, and a maximum, fmax, corresponding to the minimum and maximum applied loads.
The applied load also generates compressive or tensile stress "sgr" in the resonator beams (n=2 for double-ended tuning forks), the magnitude of which is given by the formula:
"sgr"=F/(n*b*t)
The resultant stresses must be within the elastic limits of the material and, when the transducer is used in compression, within the buckling limits of the material. The transducer is preferably highly sensitive and is stressed up to acceptable values, which defines the maximum load, Fmax, either in tension or compression. By the formulas given above, a corresponding frequency range of the resonator is found from the unstressed resonant frequency fo to the stressed frequencies fmax and fmin at the highest tensile and compressive loads on the resonator.
Various techniques have been employed to maximize the Q of these force-sensitive resonators by reducing the amount of energy lost through their mountings to the force-producing elements and structure. Flexurally vibrating beams, known as xe2x80x9cfixed-fixedxe2x80x9d beams, lose energy to the structure on which they are mounted when their reactive forces and moments are not perfectly balanced or filtered effectively. Vibration isolation systems act as low-pass mechanical filters to reduce the amount of lateral flexural energy lost by single beam resonators, as described in U.S. Pat. Nos. 3,470,400, 4,656,383, 4,658,174, 4,658,175, 4,743,790, 4,838,369, 4,980,598, 5,109,175, and 5,334,901. Double-Ended Tuning Forks (DETF) depend on the cancellation of lateral forces and moments between two symmetric beams vibrating in 180 degrees phase opposition.
Lateral flexing of vibrating beam resonators causes a longitudinal shortening for each half of a flexing cycle, therefore generating longitudinal pumping forces at twice the lateral flexing frequency. These pumping forces transfer energy to the structure on which the beams are mounted, thereby reducing the Q of such resonators. U.S. Pat. No. 4,321,500 discloses an isolation system that reduces the magnitude of such longitudinal pumping. U.S. Pat. No. 4,724,351 describes DETF sensors that are configured to minimize the longitudinal pumping by making the beams vibrate symmetrically.
U.S. Pat. No. 4,372,173 discloses a geometrical and dimensional selection process for force-sensitive resonators, which avoids spurious modes of oscillation within the resonator itself that would otherwise result in output discontinuities over the operational force range. However, even if these internal spurious modes of the resonator are avoided, residual lateral and longitudinal forces and moments remain due to imperfections in the manufacturing processes and the inability of mechanical isolation systems to totally eliminate these imbalanced forces and moments. Thus, force-sensitive resonators, including those designed according to the teachings of U.S. Pat. No. 4,372,173, apply lateral forces and moments at resonant frequency, f, and longitudinal forces and moments at double frequency, 2f, to the resonator mounting pads and thence to the force-producing structure. To a lesser degree, and dependent on mounting accuracies, the resonant frequency, f, can also be transmitted in the longitudinal direction, and the double frequency, 2f, can be transmitted in the lateral direction to the force-producing structure. As described in the U.S. Pat. No. 4,384,495, the DETF sensors must be symmetrically loaded to prevent spurious modes of oscillation that result from load-dependent differences in resonant frequencies of each beam overcoming the coupling between the two beams.
If the frequencies of the resonator""s lateral and longitudinal forces and moments that are transmitted to the force-producing mechanism coincide with resonant frequencies of the force-producing mechanism, then enough energy can be lost from the resonator to produce discontinuities in output over the operating range. Indeed, enough energy could be lost to cease oscillation of the resonator. Even if insufficient energy is lost to stop the resonator from oscillating, the resonant force-producing mechanism has a tendency to xe2x80x9cpullxe2x80x9d the resonant frequency of the resonator toward the resonant frequency of the force-producing mechanism when the resonant frequency of the resonator is close to the resonant frequency of the mechanism. This phenomenon produces a discontinuity in the relationship between the resonant frequency of the resonator and the force that is being measured by the resonator. As a result, the resonator exhibits areas of reduced accuracy when it oscillates near the resonant frequency of the force-producing mechanism.
A number of transducers have been developed which employ force-sensitive resonators to measure pressure, temperature, acceleration, angular rate, and loads. Load cells and scales employing resonators are described in U.S. Pat. Nos. 4,526,247, 4,751,849, and 4,838,369. A digital temperature sensor employing a force sensitive resonator is disclosed in U.S. Pat. No. 4,448,546. In these applications, the mechanical impedance mismatches between the resonators and force-producing mechanism are large. The high structural spring rates and correspondingly high structural resonant frequencies allow relatively easy avoidance of spurious resonances which would coincide with the frequencies of oscillation of the force-sensitive resonators.
Accelerometers and rate sensors employing resonators are disclosed in U.S. Pat. Nos. 5,974,879, 5,962,784, 5,696,323, 5,334,901, and 4,479,385. In general, these structures consist of softly suspended proof masses with structural resonant frequencies much lower than those of the force-sensitive resonators.
Pressure transducers and load sensors described in U.S. Pat. Nos. 4,382,385 and 4,406,966 employ soft bellows as the force-producing or isolating elements. Thus, these lower-frequency structural resonances are generally not excited by the lateral and longitudinal oscillations of the force-sensitive resonators. However, pressure transducers as described in U.S. Pat. No. 4,455,874 that employ lightweight structures as the force-producing elements are extremely susceptible to being excited by the lateral and longitudinal pumping of the resonators over the operational pressure range. These structures produce loads under applied pressure that change the frequencies of oscillation of the force-sensitive resonators. The pressure-responsive structures can be of the form of flattened, coiled tubes, commonly referred to as Bourdon tubes. The geometry and dimensions of the force-generating elements in these prior art transducers are such that structural resonances in the Bourdon tubes are excited by the force-sensitive resonators. Such structural excitations and subsequent energy loss produce discontinuities in the resonator output. Structural resonances occur at discrete values and harmonic overtones of the lowest modes. The difficulty of establishing clear zones, i.e., oscillation frequency ranges that will not result in spurious resonances, increases with the requirements of designing high-resolution, extremely sensitive digital pressure transducers because the more sensitive resonators have a larger frequency excursion under full-scale loads. These frequency excursions, being larger, are more likely to overlap resonant frequencies of structures, such as pressure-responsive elements, to which they are attached. Furthermore, the design of the dimensions and geometry of the pressure-responsive elements is constrained so that they generate substantial full-scale loads while being unaffected by the lateral and longitudinal excitation of the force-sensitive resonators.
The problem of resonators exciting structural resonances in Bourdon tubes is not the only problem with such pressure transducers. Another problem is the coupling of energy to mounting structures for the transducer. For example, prior art designs, such as described in U.S. Pat. No. 4,455,874, that employ xe2x80x9cUxe2x80x9d-shaped Bourdon tubes with pressure inlet ports in the plane of the tubes, easily transmit vibrations to attached base structures. Similarly, pivotally mounted structures as described in U.S. Pat. No. 4,455,874 readily transmit energy between the resonator and Bourdon tube.
In the past, there have been two approaches that have been used with some success to prevent spurious resonances from being generated in Bourdon tube transducers. One approach, which is described with reference to FIG. 3, is to use a mass-balance arrangement that can be adjusted in such a way as to change the resonant frequency of the pressure-sensitive mechanism. With trial and error, it is possible to choose the size and position of the balance weights until frequencies of the resonances move out of range. This approach usually only works with Bourdon tubes that have a coil diameter of less than 1.4 cm. It is well known that the relative spacing of the frequencies of higher harmonics decreases. This is well known in musical instruments as the higher harmonics jump from an octave to a fifth, fourth, third, etc. In a cantilevered beam (the present invention describes pressure-sensitive tubes that are generally curved cantilevered beams with various boundary conditions), the spacing of the first five modes is 3.52, 22 (525%), 61.7 (180%), 121 (96%), 200 (65%), where the increase in frequency percentage-wise becomes increasingly smaller. Depending on the boundary conditions, the spacing typically decreases by 1/n (where n is the mode). For larger devices, the higher harmonics increasingly fall into the range of the resonator frequencies. The present invention is especially useful in making highly sensitive and accurate pressure transducers that are free of output discontinuities with a length of the pressure-responsive element larger than 4 cm.
As shown in FIG. 3, a conventional transducer 20 is formed by a load-sensitive resonator 21 attached to a C-shaped Bourdon tube 25. When pressure is applied to a port 27 of the C-shaped Bourdon tube 25, the tube 25 applies bending forces to the resonator 21. The change in the operating frequency of the oscillator circuitry, which is equal to the resonant frequency of the resonator 21, is indicative of the applied pressure. In the example shown, the resonator 21 is in tension, and the frequency increases as pressure is applied. If, on the other hand, the resonator 21 is repositioned to location 22 so that it is attached between a fixed base 28 and the closed end of the Bourdon tube 23, the load can also be applied in compression, and the resonant frequency would decrease. Depending on the dimensional parameters and material strength, the ratio of generated force to applied pressure can fall over a very wide range. The relationship is well known for most tube designs, as described in xe2x80x9cAn Elementary Theory of the Bourdon Gagexe2x80x9d, by Alfred Wolf, Journal of Applied Mechanics, Trans. ASME, Vol. 68, p. A-207, September 1946 and xe2x80x9cElastic Elements of Instrumentsxe2x80x9d, by L.E. Andreeva, 1966. A conventional mass-balance arrangement 29 is used, which can be designed to perform two functions. First, the mass-balance arrangement 29 can reduce the sensitivity of the transducer to orientation errors in earth""s gravity field. Second, the additional masses are adjusted by trial and error to move spurious resonances of the tube 25 out of the full-scale frequency range of the force-sensitive resonator. The use of a mass-balance arrangement 29 can be satisfactory for relatively small transducers, but it does not work well for larger transducers for reasons that will now be explained further. The fundamental resonant frequency of a pressure-sensitive structure like a Bourdon tube is essentially proportional to the square root of k/m, where k is the stiffness of the structure and m is the mass located at the tip of the structure, which is primarily composed of the mass-balance weights. For larger transducers, i.e., those having a Bourdon tube length in excess of 4 cm, the mass-balance weights located at the ends of the structure become less important because the higher harmonics depend more on the distributed mass of the structure. Consequently, mass-balance weights cannot be used effectively to move resonances in the larger Bourdon tubes.
The second approach to preventing spurious resonances from being generated in Bourdon tube transducers is to design the Bourdon tube so that it does not have a resonant frequency within the range of resonant frequencies of the resonator over the full operating range of the Bourdon tube. This approach must be used in the design of the conventional pressure transducer 30 shown in FIG. 4. The pressure transducer 30 includes a force-sensitive resonator 33 that extends between closed ends of a U-shaped Bourdon tube 35. Pressure is applied to the Bourdon tube 35 through a centrally located tubular pressure port 37 to apply a pressure-induced tensile load on the resonator 33. The structure and dimensions of the Bourdon tube 35 may be such that the Bourdon tube 35 may resonate at frequencies that are in the operating range of the resonator 33. As a result, the Bourdon tube 35 will tend to xe2x80x9cpullxe2x80x9d the resonant frequency of the resonator 33 toward the resonant frequency of the Bourdon tube 35 when the frequency of the resonator 33 is close to the resonant frequency of the Bourdon tube 35. The transducer 30 will then provide erroneous pressure measurement when the force applied to the resonator 33 causes it to resonate near the resonant frequency of the Bourdon tube 35. FIG. 5 is a chart that shows the deviation (error) of linearized frequency output from applied pressure over the operating pressure range of the transducer 30. The presence of a spurious structural resonance shifts the frequency in a discontinuous fashion when the force applied to the resonator 33 causes its resonant frequency to be near the resonant frequency of the Bourdon tube 35, thus limiting the accuracy of the transducer 30.
As mentioned above, Bourdon tubes have been designed so that they do not have a resonant frequency within the range of resonant frequencies of the resonator. According to this approach, the dimensions of the Bourdon tube are chosen so that any resonant frequency of the Bourdon tube is outside the resonant frequencies of the resonator over the entire operating range of the transducer. In the past, these regions that are free of overlapping resonances have been found by trial and error. However, the size of these regions decreases as the diameter of the Bourdon tube coil increases. For this reason, the conventional approach of selecting the dimensions of Bourdon tubes by trial and error has been satisfactorily for relatively small Bourdon tubes, again, having a length of approximately 4 cm or less, but it has not proven satisfactory for transducers using larger Bourdon tubes. Although C-shaped and U-shaped Bourdon tubes are shown in FIGS. 3 and 4, respectively, it is understood that the same limitations and problems apply to other pressure-sensitive structures, such as helical tubes (including those with coil angles greater than 360 degrees) and spiral tubes.
Another problem with the prior art transducer 30 shown in FIG. 4 is that it couples a relatively large amount of energy through a pressure port 37 to structures on which the transducer 30 is mounted. The pressure port 37 couples vibrations axially along the length of the pressure port 37 because the pressure port 37 is within the plane of the tube 37. Since the pressure port 37 is not very compliant axially, it couples energy to mounting structures with relative ease. Thus, if the Bourdon tube 35 has any resonances within the operating range of the resonator 33, the relatively large coupling of energy from the resonator 33 to the Bourdon tube 35 that is inherent in the design of the transducer 30 magnifies the severity of the above-described problem.
Another problem with the prior art transducer shown in FIG. 8 is that the pivotally mounted suspension arm readily transmits energy from the resonator to the Bourdon tube and base structure.
As a result of these problems and limitations, there has heretofore been no suitable technique for designing highly sensitive and accurate pressure transducers having relatively large Bourdon tubes that are free of structural resonances, and, as a result, no such transducers have been available.
A pressure transducer includes a pressure vessel receiving a differential pressure that causes the vessel to deform responsive to pressure changes. A force-sensitive resonator, such as a double-ended tuning fork, is coupled to the pressure vessel so that the force exerted on the resonator by the pressure vessel is a function of the differential pressure. The resonant frequency of the resonator is thus indicative of the magnitude of the differential pressure. According to one aspect of the invention, the pressure vessel is a curved tube having a length of at least 4 cm, and the dimensions, geometry and composition of the tube are chosen so that there are no structural resonances in the pressure vessel at any resonant frequency of the resonator throughout the operating range of the transducer. In another aspect of the invention, the pressure vessel is a Bourdon tube that deforms within a bending plane responsive to a differential pressure. An elongated pressure port coupled to the pressure vessel intersects the pressure vessel along a longitudinal axis that is substantially out of the bending plane of the pressure vessel. The pressure port is relatively compliant in the lateral direction so that relatively little energy from the resonator is transferred to a mounting structure to which the pressure port is attached. In another aspect of the invention, the Bourdon tube is attached to a pivotally mounted suspension arm and is mechanically isolated from the force-sensitive resonator by masses and springs which act as a low-pass mechanical filter.